(a) Find P (b) Determine its F (x). (c) The price of the mixture depends on the contents of its alcohol. If the selling price is RM10 per gallon, otherwise it can be sold at RM8 per gallon. If the cost is RM4 per gallon, find the expected net profit for a gallon of the mixture.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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6. The percentage of alcohol (100X) in a mixture can be considered as a random variable
with p.d.f.
f(x) = 20x' (1–x), 0<x<1.
(a) Find P X <
(b) Determine its F (x).
The price of the mixture depends on the contents of its alcohol. If
the
selling price is RM10 per gallon, otherwise it can be sold at RM8 per gallon. If the
cost is RM4 per gallon, find the expected net profit for a gallon of the mixture.
Transcribed Image Text:6. The percentage of alcohol (100X) in a mixture can be considered as a random variable with p.d.f. f(x) = 20x' (1–x), 0<x<1. (a) Find P X < (b) Determine its F (x). The price of the mixture depends on the contents of its alcohol. If the selling price is RM10 per gallon, otherwise it can be sold at RM8 per gallon. If the cost is RM4 per gallon, find the expected net profit for a gallon of the mixture.
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